# How to determine failure on Mohrs Circle

• EzaMoo
In summary, on a Mohr's circle, you can determine if failure has occurred by obtaining the maximum and minimum principal stress and computing the von Mises stress using those values. Then, calculate the stress level w.r.t. yielding and if it is ≤ 100%, the component is adequate. If it is > 100%, failure has occurred. For design, the yield factor of safety should be greater than 1.0 and for failure analysis, it should be equal to 1.0. Keep in mind that this failure theory only applies to isotropic, ductile materials and other material types require different failure theories.
EzaMoo
I have already drawn the circle and am happy and confident with it, but the question asks me to determine if failure has occurred and I am unsure of how to tell, I guess I don't know how to read the circle and interpret what it means.

Can anyone describe to me how you tell if failure has occurred on a mohrs circle.

EzaMoo: I assume this is ductile material. You could obtain the maximum and minimum principal stress from your Mohr circle. Then compute von Mises stress, sigma_vm, using sigma1 and sigma3. Then compute the stress level w.r.t. yielding, Ry = FSy*sigma_vm/Sty, where FSy = yield factor of safety, and Sty = material tensile yield strength. If Ry ≤ 100 %, the analysis indicates the component is adequate. If Ry > 100 %, the analysis indicates failure.

For design, FSy > 1.0. For failure analysis only, not design, FSy = 1.0.

Keep in mind, the above failure theory (von Mises theory) applies only to isotropic, ductile materials, such as isotropic, ductile metals. Other material types require different failure theories. You must use a failure theory applicable to your material type.

## 1. How do you plot a point on Mohr's Circle?

To plot a point on Mohr's Circle, you first need to determine the principal stresses (σ1 and σ2) and the maximum shear stress (τmax) for a given state of stress. Then, using a protractor and ruler, you can plot the point by measuring the angle of rotation (2θ) on the horizontal axis and the shear stress (τ) on the vertical axis.

## 2. What is the significance of the center of Mohr's Circle?

The center of Mohr's Circle represents the average normal stress (σavg) and the average shear stress (τavg) for a given state of stress. It is also known as the center of the stress circle, and the distance from the center to any point on the circle represents the maximum shear stress (τmax).

## 3. How do you determine failure on Mohr's Circle?

To determine failure on Mohr's Circle, you need to draw a line from the center of the circle to the point representing the state of stress for the material in question. If this line intersects the circle at a point beyond the yield point, then failure will occur.

## 4. What is the difference between a normal stress and a shear stress on Mohr's Circle?

A normal stress (σ) is a force applied perpendicular to the cross-sectional area of a material, while a shear stress (τ) is a force applied parallel to the cross-sectional area. On Mohr's Circle, the normal stress is represented on the horizontal axis, while the shear stress is represented on the vertical axis.

## 5. How can Mohr's Circle be used to analyze material strength?

Mohr's Circle is a graphical representation of the state of stress for a material. By plotting the principal stresses and maximum shear stress on the circle, we can determine the maximum stress that the material can withstand before failure occurs. It can also be used to compare the strength of different materials and to predict the location and type of failure in a material under different states of stress.

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